The present invention relates to an analog filter for use in a signal readout system for a magnetic or magneto-optical disk, for example.
As magnetic/magneto-optical disk technologies have been remarkably developed in recent years, it has become increasingly necessary to further improve the signal processing technology applicable to reading signals therefrom.
FIG. 12 illustrates a known magnetic/magneto-optical disk signal readout system. A signal, read out from a disk 80, is amplified by an amplifier 81 first, and then passed through an analog filter 82 so as to have its noise reduced and its gain boosted. As used herein, “gain boosting” means a signal processing technique of sharpening the edges of a signal by boosting the high-frequency components thereof. Then, the analog output signal of the analog filter 82 is converted into a digital signal by a data slicer 83. A recent system sometimes decodes an A/D converted signal by a maximum likelihood method. Even in such a system, however, the performance required for its analog filter is much the same.
FIG. 13 illustrates ordinary frequency characteristics of an analog filter for use in a signal readout system for a magnetic or magneto-optical disk. In constructing a signal readout system for a magnetic or magneto-optical disk, its analog filter is usually designed using a Bessel filter or an equal-ripple filter so as to sharpen the signal edges and so as not to distort the signal waveform. This is because should the analog filter distort the signal waveform, the locations of the signal edges displace, thus possibly causing errors in digitizing a signal using a data slicer.
Accordingly, an analog filter is designed such that its transfer function H(s) is given by the following Equation (1)H(s)=(1−s2)/D(s)=(1+ω2)/D(jω)  (1)where s is a Laplace variable and D(s) is a function representing the denominator of the transfer function of the analog filter. In this case, the numerator of the transfer function H(s) has no imaginary part and therefore does not affect the phase characteristic of the analog filter. In addition, since the high-frequency gain is boosted by the term ω2, the gain-boosted characteristic such as that illustrated in FIG. 13 is obtained.
A filter with the gain-boosted characteristic such as that illustrated in FIG. 13 is implementable by a cascade of biquadratic filters such as those illustrated in FIG. 14. A biquadratic filter usually has quadratic poles. However, if two such filters are cascaded as shown in FIG. 14, then quadratic poles and first zeroes can be easily made in their transfer function. That is to say, the transfer function of each of the biquadratic filters shown in FIG. 14 is given by the following Equation (2):H1(s)=(gm1·gm2+sC2·gm1x)/(gm22+sC·gm3+s2C1C2) (2)  (2)Thus, the transfer function H(s) of the cascade of the two biquadratic filters shown in FIG. 14 is given by the following Equation (3):H(s)={(gm1·gm2)2−s2}/(gm22+sC2·gm3+s2C1C2)2  (3)In this manner, a transfer function having no imaginary part in its numerator and yet having the term ω2 can be obtained, thus easily realizing the gain-boosted characteristic.
A filter network implemented as a cascade of biauadratic filters, however, has its characteristic easily affected by the variation of its components.
FIG. 15 illustrates a Laplace plane representing the characteristic of an analog filter. The characteristic of an analog filter can usually be represented using a collection of poles and zeroes on a Laplace plane. In the following description, however, the characteristic of an analog filter will be regarded as a consisting of poles for the sake of simplicity.
As shown in FIG. 15, a frequency vector is represented as s=jω and its end point rises along the imaginary axis of the Laplace plane as the frequency increases. On the other hand, the frequency characteristic of an analog filter is given byH(s)=Πk=1n1/(s−sk)where sk is a vector representing the position of each pole on the Laplace plane. Thus, a frequency gain is an inverse of the product of the vector (s−sk). That is to say, the frequency characteristic of an analog filter is more likely to be affected by a relatively short vector (s−sk). In other words, the frequency characteristic of the filter is affected most by the position of a pole Sk that is closest to the imaginary axis. Also, the position of a pole displaces on the Laplace plane due to the characteristic variations of filter components.
In an analog filter network implemented as a cascade of biquadratic filters, a pair of poles is realized by each of these biquadratic filters. Thus, as shown in FIG. 16(a), the characteristic variation of a biquadratic filter BQ1 realizing the pairs of poles closest to the imaginary axis is a key factor of the variable characteristic of the analog filter network. Accordingly, the frequency characteristic of such a cascade of biquadratic filters is easily affected by the characteristic variation of its components.
An analog filter may also be implemented as a ladder filter. In a ladder filter, capacitors and inductors are connected together in a ladder shape and its input and output are terminated with resistors. In an LSI, an inductor is usually non-implementable, and therefore is replaced with an equivalent circuit including voltage-controlled current sources and capacitors, thereby constructing a ladder filter. In such a case, the ladder filter is implemented with plural biquadratic filters all coupled together.
Accordingly, in a ladder filter, the positions of all the poles are affected by the characteristic variations of its components. Thus, as shown in FIG. 16(b), if the characteristics of its components vary, then the positions of all the poles change. However, the magnitude of the displacement itself is much smaller compared to the cascade of biquadratic filters. Also, the displacement of the poles closest to the imaginary axis, which affects the frequency characteristic most seriously, becomes relatively small, too. Accordingly, the ladder filter does not have its characteristic affected by the characteristic variations of its components so much as the cascade of biquadratic filters.
However, the ladder filter is essentially a filter network of passive components. Thus, it has been widely believed that it is difficult to increase its gain to ½ or more or to realize the gain-boosted characteristic as illustrated in FIG. 13.